FORMALLY INTEGRALLY CLOSED DOMAINS AND THE RINGS R((X)) AND R{{X}}
SCIE
SCOPUS
- Title
- FORMALLY INTEGRALLY CLOSED DOMAINS AND THE RINGS R((X)) AND R{{X}}
- Authors
- Anderson, DD; Kang, BG
- Date Issued
- 1998-02-01
- Publisher
- ACADEMIC PRESS INC
- Abstract
- Let R be an integral domain. For f is an element of R[X] let A(f) be the ideal of R generated by the coefficients of f. We define R to be formally integrally closed double left right arrow (A(fg))(t) = (A(f)A(g)), for all nonzero f, g is an element of R[X]. Examples of formally integrally closed domains include locally finite intersections of one-dimensional Prufer domains (e.g., Krull domains and one-dimensional Prufer domains). We study the rings R((X)) = R[X](N) and R{{X}} = R[X](Nt) where N = (f is an element of R[X]A(f) = R) and N-t = (f is an element of R[X](A(f)) = R). We show thar R is a Krull domain (resp., Dedekind domain) double left right arrow R{{X}}(resp., R((X))) is a Krull domain (resp., Dedekind domain) double left right arrow R{{X}}(resp., R((X))) is a Euclidean domain double left right arrow every(principal) ideal of R{{X}} (resp., R((X))) is extended from R double left right arrow R is formally integrally closed and every prime ideal of R{{X}} (resp., R((X))) is extended from R. (C) 1998 Academic Press.
- Keywords
- MULTIPLICATION DOMAINS; IDEALS; R(X)
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/21129
- DOI
- 10.1006/jabr.1997.7262
- ISSN
- 0021-8693
- Article Type
- Article
- Citation
- JOURNAL OF ALGEBRA, vol. 200, no. 1, page. 347 - 362, 1998-02-01
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